If it's a nice day, visit the Arb. It's basically a huge park, with a river and everything. It's a really nice walk on a nice day. Gives you a glimpse into the quieter side of Ann Arbor:
Map:
http://maps.google.com/maps?f=q&hl=e...m=1&iwloc=addr
Look at the calendar for the school of music, to see what kind of free events there are. Also, the University's Events calendar. It sounds like you'll be here on the weekend of May 2nd. On May 3rd, there's a Musical Theater Senior Showcase, but it costs money. They're very good though. The Michigan Music school is one of the best of the country, and it looks like this is something they want to take to NYC, so it's probably quite good.
http://uuis.umich.edu/events/index.cfm?date=5/3/2009
Ditch the car! Drive down Main Street, park in a garage, and spend the day on foot. Most of the best stuff to see is all within walking distance (though some may be a long walk, you'll gain a great appreciation for the city and campus both).
The main areas are:
Main Street: the area along Main Street from William Street in the south to Ann Street in the North. There's a number of shops, restaurants, bars, etc. The main street area also extends to the east till about 4th or 5th avenue.
State Street: Take Liberty from Main Street heading east, and you will hit the State street area. There's everything from stores like the flagship Borders, to coffee shops and restaurants. If you feel like ice cream, grab a Ben and Jerry's or Stucchi's. If you feel like a drink, Ashley's is a great pub that's close to campus but yet has a classy vibe.
At the corner of State Street and North University, if you head southeast along the paths and go between the buildings, you end up in the diag. This is like the heart of the UM campus. If you follow the diag straight through, you end up at the corner of South University and East University. This is primarily a student area (where the undergrads go out at night), but it's worth a look.
There's a Michigan softball game on both May 2nd and May 3rd. Tickets are only like 5 dollars for adults.
Basically, you don't have to spend a lot of money to enjoy yourself. Take in a sporting game. Walk around the Main Street, State Street areas. Maybe take in that show I mentioned. Visit the arb (free). I know some places on Main Street have good happy hour specials. Grizzly Peak (main) has $2 homebrewed pints after 11 PM. Cafe Habana (main) has a happy hour from 3-6 PM if you're looking earlier. Go look at the stadium (Main and Hoover Street areas) While you can't get inside now due to construction, it's quite a sight to see.
But mainly, just walk. You will enjoy yourself far more if everything you do is walking.
Also, if you do go out for a nice dinner, the first weekend in May is graduation. While this shouldn't be a problem, if you plan on eating out somewhere really nice, you may wish to get a reservation just to be sure.
Hope that helps!